How did the Koran dictate that Christians should be treated by their Islamic rulers?

With love, care and respect. In the Qu'ran, Christians are often referred to as among the "People of the Book," meaning the people who have received and believed in revelations from God's prophets. The Qu'ran contains verses that highlight the commonalities between Christians and Muslims but contains other verses warning Christians against sliding toward polytheism due to their worship of Jesus Christ as God.
Here’s a few examples:
"Surely those who believe, and those who are Jews, and the Christians, and the Sabians—whoever believes in God and the Last Day and does good, they shall have their reward from their Lord. And there will be no fear for them, nor shall they grieve" (2:62, 5:69, and many other verses).
". . . and nearest among them in love to the believers will you find those who say, 'We are Christians,' because amongst these are men devoted to learning and men who have renounced the world, and they are not arrogant" (5:82).